To follow up, I re-ripped the ISOs and then compressed them with UMDGen. Still didn't work, although with my new build I was able to pull them directly off with a USB cable.
I then tried compressing them with PSP ISO Compressor, and now they work.
I'm pretty sure that compressing PSP games damages them. Like, that the program looks around inside the ISO and says "Oh look, I found a recognized audio/video file. I'm sure nobody minds if I cut it's bitrate in half." A good clue that you're working with lossy compression is that there's no way to change the file back to it's original state. Once the data is gone, it's gone.
The specific games that you're trying this with apparently don't like it when you tinker haphazardly with their innards. PSP ISO Compressor did something differently than UMDGen did, so you're not seeing the same problem in the same spot, but your games are probably still broken, you just haven't triggered their collapse yet.
It's best to use clean ISOs in your PSP. If you don't have a lot of space on your Memory Stick, store the games you're not immediately playing on your PC. If you don't have a lot of space on your PC's hard drive, compress your ISO collection safely with a "real" compression tool like WinRAR or 7-Zip.